Rapid Generation of Accurate Entry Landing Footprints

Rapid and reliable generation of the landing footprint of an entry vehicle is the key capability required for onboard determination of landing options. Under the conventional formulation of the maximum-crossrange problem at specified downranges, the footprint problem is difficult to numerically solve. When inequality trajectory constraints are imposed, accurate determination of footprints becomes even more challenging. Using the quasi-equilibrium glide condition in entry flight, a near-optimal closed-form bank angle control law is first developed for the class of problems, including the maximum-crossrange problem. Then, it is shown that the footprint problem is equivalent to seeking the solutions of a series of much simpler problems of the closest approach to a moving virtual target. The closest-approach problem is a univariate root-finding problem using the near-optimal control law. Common inequality entry trajectory constraints are enforced, without any additional difficulty, with appropriate velocity-dependent bounds of the bank angle by using the quasi-equilibrium glide condition. As a result, an accurate and fully constrained landing footprint from any feasible initial condition can be obtained rapidly and very reliably. The validity of the method is verified with independent trajectory optimization software. Footprints for an entry vehicle in several different mission scenarios and constraint settings are generated to demonstrate the method.